Ordinary muon capture studies for the matrix elements in $\beta \beta$ decay

Precise measurement of $\gamma$-rays following ordinary (non-radiative) capture of negative muons by natural Se, Kr, Cd and Sm, as well as isotopically enriched ${}^{48}$Ti, ${}^{76}$Se, ${}^{82}$Kr, ${}^{106}$Cd and ${}^{150}$Sm targets was performed by means of HPGe detectors. Energy and time distributions were investigated and total life time of negative muon in different isotopes was deduced. Detailed analysis of $\gamma$-lines intensity allows to extract relative yield of several daughter nuclei and partial rates of ($\mu$,$\nu$) capture to numerous excited levels of the ${}^{48}$Sc, ${}^{76}$As, ${}^{82}$Br, ${}^{106}$Ag and ${}^{150}$Tc isotopes which are considered to be virtual states of an intermediate odd-odd nucleus in 2$\beta$-decay of ${}^{48}$Ca, ${}^{76}$Ge, ${}^{82}$Se, ${}^{106}$Cd and ${}^{150}$Nd, respectively. These rates are important as an experimental input for the theoretical calculation of the nuclear matrix elements of 2$\beta$-decay.